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The Behaviour of Aging Functions in One-Dimensional Bouchaud's Trap Model

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Abstract

Let τ i be a collection of i.i.d. positive random variables with distribution in the domain of attraction of an α-stable law with α<1. The symmetric Bouchaud's trap model on ℤ is a Markov chain X(t) whose transition rates are given by w xy =(2τ x )−1 if x, y are neighbours in ℤ. We study the behaviour of two correlation functions: ℙ[X(t w +t)=X(t w )] and It is well known that for any of these correlation functions a time-scale t=f(t w ) such that aging occurs can be found. We study these correlation functions on time-scales different from f(t w ), and we describe more precisely the behaviour of a singular diffusion obtained as the scaling limit of Bouchaud's trap model.

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  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117, Berlin, Germany

    Jiří Černý

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  1. Jiří Černý
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Correspondence to Jiří Černý.

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Communicated by M. Aizenman

Work supported by DFG Research Center Matheon ``Mathematics for key technologies''

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Černý, J. The Behaviour of Aging Functions in One-Dimensional Bouchaud's Trap Model. Commun. Math. Phys. 261, 195–224 (2006). https://doi.org/10.1007/s00220-005-1447-x

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  • DOI: https://doi.org/10.1007/s00220-005-1447-x

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